Question: A circle has a radius of ${10}$. An arc in this circle has a central angle of $72^\circ$. What is the length of the arc? Either enter an exact answer in terms of $\pi$ or use $3.14$ for $\pi$ and enter your answer as a decimal. ${72^\circ}$ ${10}$
Explanation: First, calculate the circumference of the circle. ${72^\circ}$ ${10}$ ${20\pi}$ ${c} = 2\pi r = 2\pi ({10}) = {20\pi}$ The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{72}^\circ}{360^\circ} = \dfrac{{s}}{{{20\pi}}}$ $\dfrac{1}{5} = \dfrac{{s}}{{20\pi}}$ $\dfrac{1}{5} \times {20\pi} = {s}$ $4\pi = {s}$ ${72^\circ}$ ${10}$ ${20\pi}$ ${4\pi}$